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A245916 Number of pairs of endofunctions f, g on [n] satisfying f(g^7(i)) = f(i) for all i in [n]. 2

%I

%S 1,1,10,159,3496,98345,3373056,729481375,187564765312,37157158911249,

%T 6404841810150400,1033733019005497151,162392131536566261760,

%U 25373998461297751027321,13879265226159974639036416,11935104515280353051806269375,7611603822558997773619173031936

%N Number of pairs of endofunctions f, g on [n] satisfying f(g^7(i)) = f(i) for all i in [n].

%H Alois P. Heinz, <a href="/A245916/b245916.txt">Table of n, a(n) for n = 0..150</a>

%p with(combinat):

%p b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,

%p expand(add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

%p x^(igcd(i, 7)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)

%p end:

%p a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2)(n), j=0..n):

%p seq(a(n), n=0..20);

%Y Column k=7 of A245910.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 06 2014

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Last modified November 27 07:28 EST 2021. Contains 349365 sequences. (Running on oeis4.)